{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,10]],"date-time":"2026-05-10T06:14:32Z","timestamp":1778393672741,"version":"3.51.4"},"reference-count":166,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2020,6,1]],"date-time":"2020-06-01T00:00:00Z","timestamp":1590969600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Research Council of Science &amp; Technology (NST) grant by the Korea government (MSIP)","award":["CAP-17-04-KRISS"],"award-info":[{"award-number":["CAP-17-04-KRISS"]}]},{"name":"Energy Technology Development Project (KETEP) grant funded by the Ministry of Trade, Industry and Energy, Republic of Korea","award":["2018201010636A"],"award-info":[{"award-number":["2018201010636A"]}]},{"name":"National Research Foundation (NRF) of Korea, funded by the Ministry of Education","award":["NRF-2018R1A6A1A03025761"],"award-info":[{"award-number":["NRF-2018R1A6A1A03025761"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Recent advances in lithography technology and the spread of 3D printers allow us a facile fabrication of special materials with complicated microstructures. The materials are called \u201cdesigned materials\u201d or \u201carchitectured materials\u201d and provide new opportunities for material development. These materials, which owing to their rationally designed architectures exhibit unusual properties at the micro- and nano-scales, are being widely exploited in the development of modern materials with customized and improved performance. Meta-materials are found to possess superior and unusual properties as regards static modulus (axial stress divided by axial strain), density, energy absorption, smart functionality, and negative Poisson\u2019s ratio (NPR). However, in spite of recent developments, it has only been feasible to fabricate a few such meta-materials and to implement them in practical applications. Against such a backdrop, a broad review of the wide range of cellular auxetic structures for mechanical metamaterials available at our disposal and their potential application areas is important. Classified according to their geometrical configuration, this paper provides a review of cellular auxetic structures. The structures are presented with a view to tap into their potential abilities and leverage multidimensional fabrication advances to facilitate their application in industry. In this review, there is a special emphasis on state-of-the-art applications of these structures in important domains such as sensors and actuators, the medical industry, and defense while touching upon ways to accelerate the material development process.<\/jats:p>","DOI":"10.3390\/s20113132","type":"journal-article","created":{"date-parts":[[2020,6,2]],"date-time":"2020-06-02T09:19:27Z","timestamp":1591089567000},"page":"3132","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":208,"title":["Cellular Auxetic Structures for Mechanical Metamaterials: A Review"],"prefix":"10.3390","volume":"20","author":[{"given":"Parth Uday","family":"Kelkar","sequence":"first","affiliation":[{"name":"Center for Electronic Materials, Korea Institute of Science and Technology (KIST), Seoul 02792, Korea"},{"name":"Mechanical Engineering, Vishwakarma Institute of Technology, Pune, Maharashtra 411037, India"}]},{"given":"Hyun Soo","family":"Kim","sequence":"additional","affiliation":[{"name":"Center for Electronic Materials, Korea Institute of Science and Technology (KIST), Seoul 02792, Korea"},{"name":"Quantum Functional Materials Laboratory, Department of Physics, Inha University, Incheon 22212, Korea"}]},{"given":"Kyung-Hoon","family":"Cho","sequence":"additional","affiliation":[{"name":"School of Materials Science and Engineering, Kumoh National Institute of Technology, Gumi 39177, Korea"}]},{"given":"Joon Young","family":"Kwak","sequence":"additional","affiliation":[{"name":"Center for Electronic Materials, Korea Institute of Science and Technology (KIST), Seoul 02792, Korea"}]},{"given":"Chong-Yun","family":"Kang","sequence":"additional","affiliation":[{"name":"Center for Electronic Materials, Korea Institute of Science and Technology (KIST), Seoul 02792, Korea"},{"name":"KU-KIST Graduate School of Converging Science and Technology, Korea University, Seoul 02841, Korea"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5563-9088","authenticated-orcid":false,"given":"Hyun-Cheol","family":"Song","sequence":"additional","affiliation":[{"name":"Center for Electronic Materials, Korea Institute of Science and Technology (KIST), Seoul 02792, Korea"}]}],"member":"1968","published-online":{"date-parts":[[2020,6,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"4773","DOI":"10.1103\/PhysRevLett.76.4773","article-title":"Extremely low frequency plasmons in metallic mesostructures","volume":"76","author":"Pendry","year":"1996","journal-title":"Phys. Rev. Lett."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"4184","DOI":"10.1103\/PhysRevLett.84.4184","article-title":"Composite medium with simultaneously negative permeability and permittivity","volume":"84","author":"Smith","year":"2000","journal-title":"Phys. Rev. Lett."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2075","DOI":"10.1109\/22.798002","article-title":"Magnetism from conductors and enhanced nonlinear phenomena","volume":"47","author":"Pendry","year":"1999","journal-title":"IEEE Trans. Microw. Theory Tech."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1038\/nmat2743","article-title":"Transformation optics and metamaterials","volume":"9","author":"Chen","year":"2010","journal-title":"Nat. Mater."},{"key":"ref_5","first-page":"103","article-title":"Photophysics of structural color in the morpho butterflies","volume":"17","author":"Kinoshita","year":"2002","journal-title":"Forma"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"S213","DOI":"10.2142\/biophys.41.S213_1","article-title":"Mechanism of the structural color in Morpho butterflies","volume":"41","author":"Kinoshita","year":"2001","journal-title":"Seibutsu Butsuri"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Choi, S.H., Ku, Z., Kim, S., Choi, K., Urbas, A.M., and Kim, Y.L. (2018, January 13\u201318). Silk is a natural metamaterial for self-cooling: An oxymoron?. Proceedings of the 2018 Conference on Lasers and Electro-Optics (CLEO), San Jose, CA, USA.","DOI":"10.1364\/CLEO_AT.2018.ATh3P.7"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Yan, Y. (2016). Developments in fibers for technical nonwovens. Advances in Technical Nonwovens, Woodhead Publishing.","DOI":"10.1016\/B978-0-08-100575-0.00002-4"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"823","DOI":"10.1038\/nmat3134","article-title":"Poisson\u2019s ratio and modern materials","volume":"10","author":"Greaves","year":"2011","journal-title":"Nat. Mater."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"260","DOI":"10.1108\/02644401211212398","article-title":"Design and optimization of microstructure of auxetic materials","volume":"29","author":"Javadi","year":"2012","journal-title":"Eng. Comput. (Swans. Wales)"},{"key":"ref_11","unstructured":"Kurtz, S.M. (2009). Uhmwpe Biomaterials Handbook, William Andrew."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1093\/qjmamj\/hbh021","article-title":"Poisson\u2019s ratio for anisotropic elastic materials can have no bounds","volume":"58","author":"Ting","year":"2005","journal-title":"Q. J. Mech. Appl. Math."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"17066","DOI":"10.1038\/natrevmats.2017.66","article-title":"Flexible mechanical metamaterials","volume":"2","author":"Bertoldi","year":"2017","journal-title":"Nat. Rev. Mater."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"124","DOI":"10.1038\/353124a0","article-title":"Molecular network design","volume":"353","author":"Evans","year":"1991","journal-title":"Nature"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1038\/s41467-017-00399-6","article-title":"Computational prediction of new auxetic materials","volume":"8","author":"Dagdelen","year":"2017","journal-title":"Nat. Commun."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"5375","DOI":"10.1007\/BF02403846","article-title":"Non-linear properties of metallic cellular materials with a negative Poisson\u2019s ratio","volume":"27","author":"Choi","year":"1992","journal-title":"J. Mater. Sci."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1016\/j.ijengsci.2012.01.010","article-title":"On local indentation and impact compliance of isotropic auxetic materials from the continuum mechanics viewpoint","volume":"54","author":"Argatov","year":"2012","journal-title":"Int. J. Eng. Sci."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1007\/BF00036481","article-title":"Fracture toughness of re-entrant foam materials with a negative Poisson\u2019s ratio: Experiment and analysis","volume":"80","author":"Choi","year":"1996","journal-title":"Int. J. Fract."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1038","DOI":"10.1126\/science.235.4792.1038","article-title":"Foam structures with a negative poisson\u2019s ratio","volume":"235","author":"Lakes","year":"1987","journal-title":"Science"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"654","DOI":"10.1021\/ie990572w","article-title":"An auxetic filter: A tuneable filter displaying enhanced size selectivity or defouling properties","volume":"39","author":"Alderson","year":"2000","journal-title":"Ind. Eng. Chem. Res."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"23001","DOI":"10.1088\/1361-665X\/aaa61c","article-title":"Auxetic metamaterials and structures: A review","volume":"27","author":"Ren","year":"2018","journal-title":"Smart Mater. Struct."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"222","DOI":"10.1038\/358222a0","article-title":"Negative Poisson ratios in crystalline SiO2 from first-principles calculations","volume":"358","author":"Keskar","year":"1992","journal-title":"Nature"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"617","DOI":"10.1002\/(SICI)1521-4095(200005)12:9<617::AID-ADMA617>3.0.CO;2-3","article-title":"Auxetic materials: Functional materials and structures from lateral thinking!","volume":"12","author":"Evans","year":"2000","journal-title":"Adv. Mater."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"5111","DOI":"10.1039\/C6RA27333E","article-title":"Auxetic mechanical metamaterials","volume":"7","author":"Kolken","year":"2017","journal-title":"RSC Adv."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"40141","DOI":"10.1021\/acsami.8b13857","article-title":"Hygroscopic auxetic on-skin sensors for easy-to-handle repeated daily use","volume":"10","author":"Kim","year":"2018","journal-title":"ACS Appl. Mater. Interfaces"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"e1706589","DOI":"10.1002\/adma.201706589","article-title":"Auxetic mechanical metamaterials to enhance sensitivity of stretchable strain sensors","volume":"30","author":"Jiang","year":"2018","journal-title":"Adv. Mater."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"75027","DOI":"10.1088\/0964-1726\/24\/7\/075027","article-title":"Design and fabrication of auxetic stretchable force sensor for hand rehabilitation","volume":"24","author":"Ko","year":"2015","journal-title":"Smart Mater. Struct."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Duncan, O., Shepherd, T., Moroney, C., Foster, L., Venkatraman, P.D., Winwood, K., Allen, T., and Alderson, A. (2018). Review of auxetic materials for sports applications: Expanding options in comfort and protection. Appl. Sci., 8.","DOI":"10.3390\/app8060941"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1016\/j.proeng.2014.06.079","article-title":"Auxetic materials for sports applications","volume":"72","author":"Sanami","year":"2014","journal-title":"Procedia Eng."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1600","DOI":"10.1177\/0040517512449051","article-title":"Auxetic materials and their potential applications in textiles","volume":"84","author":"Wang","year":"2014","journal-title":"Text. Res. J."},{"key":"ref_31","unstructured":"(2019, August 17). AZoM Auxetic Materials\u2014Applications. Available online: https:\/\/www.azom.com\/article.aspx?ArticleID=168."},{"key":"ref_32","unstructured":"Burriesci, G., and Bergamasco, G. (2007). Annuloplasty Prosthesis with an Auxetic Structure, Jouve."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"2573","DOI":"10.1007\/s10856-011-4436-y","article-title":"An Auxetic structure configured as oesophageal stent with potential to be used for palliative treatment of oesophageal cancer; Development and in vitro mechanical analysis","volume":"22","author":"Ali","year":"2011","journal-title":"J. Mater. Sci. Mater. Med."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1007\/s10856-013-5067-2","article-title":"Auxetic oesophageal stents: Structure and mechanical properties","volume":"25","author":"Ali","year":"2014","journal-title":"J. Mater. Sci. Mater. Med."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"913","DOI":"10.1007\/s11340-019-00489-0","article-title":"Mechanical properties of selective laser sintering (SLS) additive manufactured chiral Auxetic cylindrical stent","volume":"59","author":"Geng","year":"2019","journal-title":"Exp. Mech."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2014\/753496","article-title":"Review of mechanics and applications of auxetic structures","volume":"2014","author":"Mir","year":"2014","journal-title":"Adv. Mater. Sci. Eng."},{"key":"ref_37","first-page":"126","article-title":"Pyrolytic materials for thermal protection systems","volume":"22","author":"Garber","year":"1963","journal-title":"Aerosp. Eng."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"242","DOI":"10.1016\/j.compstruct.2017.03.018","article-title":"Blast resistance of auxetic and honeycomb sandwich panels: Comparisons and parametric designs","volume":"183","author":"Imbalzano","year":"2018","journal-title":"Compos. Struct."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1016\/j.compstruct.2018.11.050","article-title":"Blast response study of the sandwich composite panels with 3D chiral auxetic core","volume":"210","author":"Novak","year":"2019","journal-title":"Compos. Struct."},{"key":"ref_40","unstructured":"Ma, Z.-D., Liu, Y., Liu, X., Sun, C., and Yushun, C. (2011). Ultralightweight Runflat Tires Based upon Negative Poisson Ratio (NPR) Auxetic Structures 2010. (20110168313A1), U.S. Patent."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Scheffler, M., and Colombo, P. (2006). Cellular Ceramics: Structure, Manufacturing, Properties and Applications, Wiley-VCH Verlag GmbH & Co. KGaA.","DOI":"10.1002\/3527606696"},{"key":"ref_42","unstructured":"Gibson, L.J., and Ashby, M.F. (1989). Cellular Solids: Structure & Properties, Pergamon Press."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Mazur, M., Leary, M., McMillan, M., Sun, S., Shidid, D., and Brandt, M. (2017). Mechanical properties of Ti6Al4V and AlSi12Mg lattice structures manufactured by Selective Laser Melting (SLM). Laser Addit. Manuf., 119\u2013161.","DOI":"10.1016\/B978-0-08-100433-3.00005-1"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"266","DOI":"10.3221\/IGF-ESIS.46.24","article-title":"Micro failure analysis of adhesively bonded joints enhanced with natural cork particles: Impact of overlap length and particles volume fraction","volume":"12","author":"Barbosa","year":"2018","journal-title":"Frat. Ed Integrit\u00e0 Strutt."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Ansell, M.P. (2015). Wood microstructure-A cellular composite. Wood Composites, Woodhead Publishing.","DOI":"10.1016\/B978-1-78242-454-3.10000-9"},{"key":"ref_46","first-page":"369","article-title":"Design and Additive manufacturing of lattice-based cellular solids at building scale","volume":"3","author":"Naboni","year":"2017","journal-title":"Blucher Des. Proc."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"2797","DOI":"10.1023\/A:1018660130501","article-title":"Modelling concurrent deformation mechanisms in auxetic microporous polymers","volume":"32","author":"Alderson","year":"1997","journal-title":"J. Mater. Sci."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"372","DOI":"10.1007\/s10853-010-4846-0","article-title":"A generalised three-dimensional tethered-nodule model for auxetic materials","volume":"46","author":"Gaspar","year":"2010","journal-title":"J. Mater. Sci."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/s10999-012-9192-8","article-title":"Effective elastic properties of auxetic microstructures: Anisotropy and structural applications","volume":"9","author":"Dirrenberger","year":"2012","journal-title":"Int. J. Mech. Mater. Des."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1016\/S0263-8223(96)00054-2","article-title":"Models for the elastic deformation of honeycombs","volume":"35","author":"Masters","year":"1996","journal-title":"Compos. Struct."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"4349","DOI":"10.1016\/S1359-6454(00)00269-X","article-title":"A novel mechanism for generating auxetic behaviour in reticulated foams: Missing rib foam model","volume":"48","author":"Smith","year":"2000","journal-title":"Acta Mater."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"4406","DOI":"10.1007\/BF00551939","article-title":"Negative Poisson\u2019s ratio polymeric and metallic foams","volume":"23","author":"Friis","year":"1988","journal-title":"J. Mater. Sci."},{"key":"ref_53","first-page":"300","article-title":"Introduction to the finite element method","volume":"2","author":"Hearn","year":"1997","journal-title":"Mech. Mater."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"551","DOI":"10.1126\/science.238.4826.551.b","article-title":"Response: Negative poisson\u2019s ratio materials","volume":"238","author":"Lakes","year":"1987","journal-title":"Science"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"5945","DOI":"10.1023\/A:1018606926094","article-title":"Fabrication methods for auxetic foams","volume":"32","author":"Chan","year":"1997","journal-title":"J. Mater. Sci."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1177\/0021955X15579456","article-title":"Auxetic epoxy foams produced by solid state foaming","volume":"52","author":"Quadrini","year":"2015","journal-title":"J. Cell. Plast."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1515\/epoly-2014-0193","article-title":"Three decades of auxetic polymers: A review","volume":"15","author":"Bhullar","year":"2015","journal-title":"e-Polymers"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/0020-7403(94)00047-N","article-title":"Analysis of elastic modulus of conventional foams and of re-entrant foam materials with a negative Poisson\u2019s ratio","volume":"37","author":"Choi","year":"1995","journal-title":"Int. J. Mech. Sci."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"1193","DOI":"10.1177\/002199839302701203","article-title":"Indentability of conventional and negative poisson\u2019s ratio foams","volume":"27","author":"Lakes","year":"1993","journal-title":"J. Compos. Mater."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1007\/s11837-009-0038-2","article-title":"Micro-compression testing of fcc metals: A selected overview of experiments and simulations","volume":"61","author":"Uchic","year":"2009","journal-title":"JOM"},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1146\/annurev.matsci.36.062705.134551","article-title":"Microscale characterization of mechanical properties","volume":"37","author":"Hemker","year":"2007","journal-title":"Annu. Rev. Mater. Res."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"3523","DOI":"10.1016\/j.actamat.2008.03.036","article-title":"Determination of the effective zero-point and the extraction of spherical nanoindentation stress-strain curves","volume":"56","author":"Kalidindi","year":"2008","journal-title":"Acta Mater."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"2439","DOI":"10.1016\/j.actamat.2005.02.006","article-title":"Novel honeycombs with auxetic behaviour","volume":"53","author":"Gaspar","year":"2005","journal-title":"Acta Mater."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"925","DOI":"10.1080\/08927020500401139","article-title":"On the potential of connected stars as auxetic systems","volume":"31","author":"Grima","year":"2005","journal-title":"Mol. Simul."},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"2337","DOI":"10.1002\/adma.201104395","article-title":"Compaction through buckling in 2D periodic, soft and porous structures: Effect of pore shape","volume":"24","author":"Overvelde","year":"2012","journal-title":"Adv. Mater."},{"key":"ref_66","doi-asserted-by":"crossref","unstructured":"(1985). An isotropic three-dimensional structure with Poisson\u2019s ratio = -1. J. Elast., 15, 427\u2013430.","DOI":"10.1007\/BF00042531"},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"25013","DOI":"10.1088\/0964-1726\/24\/2\/025013","article-title":"A systematic approach to identify cellular auxetic materials","volume":"24","author":"Korner","year":"2015","journal-title":"Smart Mater. Struct."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"3370","DOI":"10.1016\/j.actamat.2012.03.015","article-title":"Compressive properties of Ti\u20136Al\u20134V auxetic mesh structures made by electron beam melting","volume":"60","author":"Yang","year":"2012","journal-title":"Acta Mater."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"2710","DOI":"10.1002\/adma.201200584","article-title":"Tailored 3D mechanical metamaterials made by dip-in direct-laser-writing optical lithography","volume":"24","author":"Stenger","year":"2012","journal-title":"Adv. Mater."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"456","DOI":"10.1016\/j.matlet.2015.11.037","article-title":"A unit cell structure with tunable Poisson\u2019s ratio from positive to negative","volume":"164","author":"Li","year":"2016","journal-title":"Mater. Lett."},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"5044","DOI":"10.1002\/adma.201301986","article-title":"3D soft metamaterials with negative poisson\u2019s ratio","volume":"25","author":"Babaee","year":"2013","journal-title":"Adv. Mater."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"5978","DOI":"10.1073\/pnas.1115674109","article-title":"Buckling-induced encapsulation of structured elastic shells under pressure","volume":"109","author":"Shim","year":"2012","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"1515","DOI":"10.1002\/pssb.201451304","article-title":"Simple cubic three-dimensional auxetic metamaterials","volume":"251","author":"Shen","year":"2014","journal-title":"Phys. Status Solidi"},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"1252","DOI":"10.1002\/pssb.201600015","article-title":"A 3D auxetic material based on intersecting double arrowheads","volume":"253","author":"Lim","year":"2016","journal-title":"Phys. Status Solidi"},{"key":"ref_75","first-page":"1","article-title":"Computational approach in formulating mechanical characteristics of 3D star honeycomb auxetic structure","volume":"2015","author":"Rad","year":"2015","journal-title":"Adv. Mater. Sci. Eng."},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"1700024","DOI":"10.1002\/pssb.201700024","article-title":"Microstructural effects on the poisson\u2019s ratio of star-shaped two-dimensional systems","volume":"254","author":"Wang","year":"2017","journal-title":"Phys. Status Solidi"},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"1877","DOI":"10.1088\/0022-3727\/22\/12\/012","article-title":"Microporous materials with negative Poisson\u2019s ratios. I. Microstructure and mechanical properties","volume":"22","author":"Caddock","year":"1989","journal-title":"J. Phys. D. Appl. Phys."},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"636","DOI":"10.1002\/pen.10451","article-title":"The effects of powder morphology on the processing of auxetic polypropylene (PP of negative poisson\u2019s ratio)","volume":"36","author":"Pickles","year":"1996","journal-title":"Polym. Eng. Sci."},{"key":"ref_79","unstructured":"Bellare, A., Bistolfi, A., Simis, K., and Pruitt, L. (2020, May 01). Physico-chemical characteristics of UHMWPE before and after processing. Available online: https:\/\/www.researchgate.net\/publication\/228588911_Physico-chemical_characteristics_of_UHMWPE_before_and_after_processing."},{"key":"ref_80","first-page":"8","article-title":"Characterization and Auxetic effect of Polytetrafluoroethylene Tubular structure","volume":"1","author":"Bhullar","year":"2014","journal-title":"Int. J. Adv. Sci. Eng."},{"key":"ref_81","doi-asserted-by":"crossref","first-page":"2671","DOI":"10.1039\/ft9959102671","article-title":"Auxetic two-dimensional polymer networks. An example of tailoring geometry for specific mechanical properties","volume":"91","author":"Evans","year":"1995","journal-title":"J. Chem. Soc. Faraday Trans."},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"2287","DOI":"10.1007\/BF01130170","article-title":"Deformation mechanisms in negative Poisson\u2019s ratio materials: Structural aspects","volume":"26","author":"Lakes","year":"1991","journal-title":"J. Mater. Sci."},{"key":"ref_83","doi-asserted-by":"crossref","first-page":"2397","DOI":"10.1038\/s41598-018-20795-2","article-title":"3D printed Auxetic mechanical metamaterial with chiral cells and re-entrant cores","volume":"8","author":"Jiang","year":"2018","journal-title":"Sci. Rep."},{"key":"ref_84","doi-asserted-by":"crossref","first-page":"1042","DOI":"10.1016\/j.compscitech.2009.07.009","article-title":"Elastic constants of 3-, 4- and 6-connected chiral and anti-chiral honeycombs subject to uniaxial in-plane loading","volume":"70","author":"Alderson","year":"2010","journal-title":"Compos. Sci. Technol."},{"key":"ref_85","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1002\/pssb.200777704","article-title":"On the properties of auxetic meta-tetrachiral structures","volume":"245","author":"Grima","year":"2008","journal-title":"Phys. Status Solidi"},{"key":"ref_86","doi-asserted-by":"crossref","first-page":"54005","DOI":"10.1088\/0964-1726\/25\/5\/054005","article-title":"Chiral three-dimensional lattices with tunable Poisson\u2019s ratio","volume":"25","author":"Ha","year":"2016","journal-title":"Smart Mater. Struct."},{"key":"ref_87","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/j.taml.2016.02.004","article-title":"Elastic properties of chiral, anti-chiral, and hierarchical honeycombs: A simple energy-based approach","volume":"6","author":"Mousanezhad","year":"2016","journal-title":"Theor. Appl. Mech. Lett."},{"key":"ref_88","doi-asserted-by":"crossref","first-page":"2012","DOI":"10.1002\/pssb.201384246","article-title":"A realistic generic model for anti-tetrachiral systems","volume":"250","author":"Gatt","year":"2013","journal-title":"Phys. Status Solidi Basic Res."},{"key":"ref_89","doi-asserted-by":"crossref","first-page":"1557","DOI":"10.1002\/pssb.201600027","article-title":"Design and properties of 3D-printed chiral auxetic metamaterials by reconfigurable connections","volume":"253","author":"Huang","year":"2016","journal-title":"Phys. Status Solidi Basic Res."},{"key":"ref_90","doi-asserted-by":"crossref","first-page":"1435","DOI":"10.1002\/pssb.201451689","article-title":"Chiral topologies for composite morphing structures\u2014Part I: Development of a chiral rib for deformable airfoils","volume":"252","author":"Airoldi","year":"2015","journal-title":"Phys. Status Solidi Basic Res."},{"key":"ref_91","doi-asserted-by":"crossref","first-page":"1446","DOI":"10.1002\/pssb.201584263","article-title":"Chiral topologies for composite morphing structures\u2014Part II: Novel configurations and technological processes","volume":"252","author":"Airoldi","year":"2015","journal-title":"Phys. Status Solidi Basic Res."},{"key":"ref_92","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1007\/s11709-016-0352-z","article-title":"Design concepts of an aircraft wing: Composite and morphing airfoil with auxetic structures","volume":"10","author":"Budarapu","year":"2016","journal-title":"Front. Struct. Civ. Eng."},{"key":"ref_93","doi-asserted-by":"crossref","unstructured":"Zhang, Z., Hu, H., Liu, S., and Xu, B. (2013). Study of an auxetic structure made of tubes and corrugated sheets. Phys. Status Solidi.","DOI":"10.1002\/pssb.201248349"},{"key":"ref_94","doi-asserted-by":"crossref","first-page":"504","DOI":"10.1126\/science.1149815","article-title":"Sign change of poisson\u2019s ratio for carbon nanotube sheets","volume":"320","author":"Hall","year":"2008","journal-title":"Science"},{"key":"ref_95","doi-asserted-by":"crossref","first-page":"65709","DOI":"10.1088\/0957-4484\/20\/6\/065709","article-title":"Effective elastic mechanical properties of single layer graphene sheets","volume":"20","author":"Scarpa","year":"2009","journal-title":"Nanotechnology"},{"key":"ref_96","doi-asserted-by":"crossref","first-page":"1455","DOI":"10.1002\/adma.201404106","article-title":"Tailoring graphene to achieve negative poisson\u2019s ratio properties","volume":"27","author":"Grima","year":"2014","journal-title":"Adv. Mater."},{"key":"ref_97","doi-asserted-by":"crossref","first-page":"1600612","DOI":"10.1002\/pssb.201600612","article-title":"Negative Poisson\u2019s ratio in non-porous smooth curve sheet","volume":"254","author":"Tan","year":"2017","journal-title":"Phys. Status Solidi"},{"key":"ref_98","doi-asserted-by":"crossref","unstructured":"Lang, R.J. (2011). Origami Design Secrets, A.K. Peters.","DOI":"10.1201\/b11074"},{"key":"ref_99","doi-asserted-by":"crossref","first-page":"3276","DOI":"10.1103\/PhysRevLett.113.245502","article-title":"Making the cut: Lattice kirigami rules","volume":"113","author":"Castle","year":"2014","journal-title":"Phys. Rev. Lett."},{"key":"ref_100","doi-asserted-by":"crossref","first-page":"3276","DOI":"10.1073\/pnas.1217998110","article-title":"Geometry of miura-folded metamaterials","volume":"110","author":"Schenk","year":"2013","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_101","doi-asserted-by":"crossref","first-page":"647","DOI":"10.1126\/science.1252876","article-title":"Using origami design principles to fold reprogrammable mechanical metamaterials","volume":"345","author":"Silverberg","year":"2014","journal-title":"Science"},{"key":"ref_102","first-page":"1","article-title":"Method of packaging and deployment of large membranes in space","volume":"618","author":"Miura","year":"1985","journal-title":"Inst. Space Astronaut. Sci."},{"key":"ref_103","doi-asserted-by":"crossref","first-page":"460","DOI":"10.1002\/adem.201000005","article-title":"Perforated sheets exhibiting negative poisson\u2019s ratios","volume":"12","author":"Grima","year":"2010","journal-title":"Adv. Eng. Mater."},{"key":"ref_104","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1002\/adma.201503653","article-title":"Auxetic perforated mechanical metamaterials with randomly oriented cuts","volume":"28","author":"Grima","year":"2015","journal-title":"Adv. Mater."},{"key":"ref_105","doi-asserted-by":"crossref","first-page":"1563","DOI":"10.1023\/A:1006781224002","article-title":"Auxetic behavior from rotating squares","volume":"19","author":"Grima","year":"2000","journal-title":"J. Mater. Sci. Lett."},{"key":"ref_106","doi-asserted-by":"crossref","first-page":"137","DOI":"10.12921\/cmst.2004.10.02.137-145","article-title":"Negative poisson\u2019s ratios from rotating rectangles","volume":"10","author":"Grima","year":"2004","journal-title":"Comput. Methods Sci. Technol."},{"key":"ref_107","doi-asserted-by":"crossref","first-page":"3193","DOI":"10.1007\/s10853-006-6339-8","article-title":"Auxetic behavior from rotating triangles","volume":"41","author":"Grima","year":"2006","journal-title":"J. Mater. Sci."},{"key":"ref_108","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1002\/pssb.200777705","article-title":"On the auxetic properties of rotating rhombi and parallelograms: A preliminary investigation","volume":"245","author":"Grima","year":"2008","journal-title":"Phys. Status Solidi"},{"key":"ref_109","doi-asserted-by":"crossref","first-page":"866","DOI":"10.1002\/pssb.200572706","article-title":"Auxetic behaviour from rotating semi-rigid units","volume":"244","author":"Grima","year":"2007","journal-title":"Phys. Status Solidi"},{"key":"ref_110","doi-asserted-by":"crossref","first-page":"711","DOI":"10.1007\/s002690100209","article-title":"Rotation and dilation deformation mechanisms for auxetic behaviour in the ?-cristobalite tetrahedral framework structure","volume":"28","author":"Evans","year":"2001","journal-title":"Phys. Chem. Miner."},{"key":"ref_111","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1016\/j.eml.2016.09.001","article-title":"Bistable auxetic mechanical metamaterials inspired by ancient geometric motifs","volume":"9","author":"Rafsanjani","year":"2016","journal-title":"Extrem. Mech. Lett."},{"key":"ref_112","doi-asserted-by":"crossref","first-page":"2395","DOI":"10.1002\/pssb.200880269","article-title":"Auxetic behaviour from rotating rhombi","volume":"245","author":"Attard","year":"2008","journal-title":"Phys. Status Solidi"},{"key":"ref_113","doi-asserted-by":"crossref","first-page":"1980","DOI":"10.1016\/j.jnoncrysol.2010.05.074","article-title":"Auxetic behaviour in non-crystalline materials having star or triangular shaped perforations","volume":"356","author":"Grima","year":"2010","journal-title":"J. Non. Cryst. Solids"},{"key":"ref_114","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1016\/j.commatsci.2012.02.012","article-title":"Seeing auxetic materials from the mechanics point of view: A structural review on the negative Poisson\u2019s ratio","volume":"58","author":"Prawoto","year":"2012","journal-title":"Comput. Mater. Sci."},{"key":"ref_115","unstructured":"Cross, T., Hoffer, K., Jones, D., Kirsvhner, P., Langvin, E., and Meschter, J. (2016). Auxetic Structures and Footwear with Soles Having Auxetic Structures. (9402439B2), U.S. Patent."},{"key":"ref_116","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/j.msea.2005.12.016","article-title":"Self-deployable origami stent grafts as a biomedical application of Ni-rich TiNi shape memory alloy foil","volume":"419","author":"Kuribayashi","year":"2006","journal-title":"Mater. Sci. Eng. A"},{"key":"ref_117","doi-asserted-by":"crossref","first-page":"75013","DOI":"10.1088\/0964-1726\/21\/7\/075013","article-title":"Deployable auxetic shape memory alloy cellular antenna demonstrator: Design, manufacturing and modal testing","volume":"21","author":"Jacobs","year":"2012","journal-title":"Smart Mater. Struct."},{"key":"ref_118","doi-asserted-by":"crossref","first-page":"344","DOI":"10.1179\/146580102225006495","article-title":"Auxetic polypropylene fibres Part 1\u2014Manufacture and characterisation","volume":"31","author":"Alderson","year":"2002","journal-title":"Plast. Rubber Compos."},{"key":"ref_119","unstructured":"Toronjo, A. (2017). Articles of Apparel Including Auxetic Materials. (20170099900A1), U.S. Patent."},{"key":"ref_120","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/j.ijimpeng.2015.04.005","article-title":"Impact resistance of uniform and functionally graded auxetic double arrowhead honeycombs","volume":"83","author":"Qiao","year":"2015","journal-title":"Int. J. Impact Eng."},{"key":"ref_121","unstructured":"(2020, April 01). Nike The New Dimensions of Nike Free. Available online: https:\/\/news.nike.com\/news\/nike-free-2016-running-training#."},{"key":"ref_122","unstructured":"(2020, April 01). D3O Trust Nimbus Helmet Pad System. Available online: https:\/\/www.d3o.com\/partner-support\/products\/trust-nimbus-helmet-pad-system\/."},{"key":"ref_123","doi-asserted-by":"crossref","first-page":"103291","DOI":"10.1016\/j.mechmat.2019.103291","article-title":"2D triangular anti-trichiral structures and auxetic stents with symmetric shrinkage behavior and high energy absorption","volume":"142","author":"Hamzehei","year":"2020","journal-title":"Mech. Mater."},{"key":"ref_124","doi-asserted-by":"crossref","first-page":"578","DOI":"10.1007\/s11431-019-1468-2","article-title":"4D printing of personalized shape memory polymer vascular stents with negative Poisson\u2019s ratio structure: A preliminary study","volume":"63","author":"Lin","year":"2020","journal-title":"Sci. China Technol. Sci."},{"key":"ref_125","unstructured":"Wang, B., Zhang, C., Zeng, C., Kramer, L.D., and Gillis, A. (2013). Prosthetic Socket Apparatus And Systems. (9486333B2), U.S. Patent."},{"key":"ref_126","doi-asserted-by":"crossref","unstructured":"Paxton, N.C., Daley, R., Forrestal, D.P., Allenby, M.C., and Woodruff, M.A. (2020). Auxetic tubular scaffolds via melt electrowriting. Mater. Des.","DOI":"10.1016\/j.matdes.2020.108787"},{"key":"ref_127","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1007\/s42242-020-00066-8","article-title":"A new design of 3D-printed orthopedic bone plates with auxetic structures to mitigate stress shielding and improve intra-operative bending","volume":"3","author":"Vijayavenkataraman","year":"2020","journal-title":"Bio-Design Manuf."},{"key":"ref_128","doi-asserted-by":"crossref","first-page":"108424","DOI":"10.1016\/j.matdes.2019.108424","article-title":"A novel auxetic structure based bone screw design: Tensile mechanical characterization and pullout fixation strength evaluation","volume":"188","author":"Yao","year":"2020","journal-title":"Mater. Des."},{"key":"ref_129","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1002\/admt.201900452","article-title":"3D printing ionogel auxetic frameworks for stretchable sensors","volume":"4","author":"Wong","year":"2019","journal-title":"Adv. Mater. Technol."},{"key":"ref_130","doi-asserted-by":"crossref","first-page":"085037","DOI":"10.1088\/1361-665X\/aa7772","article-title":"Auxetic behavior and acoustic properties of microstructured piezoelectric strain sensors","volume":"26","author":"Bacigalupo","year":"2017","journal-title":"Smart Mater. Struct."},{"key":"ref_131","doi-asserted-by":"crossref","first-page":"2900","DOI":"10.1002\/adfm.201505070","article-title":"Poisson ratio and piezoresistive sensing: A new route to high-performance 3D flexible and stretchable sensors of multimodal sensing capability","volume":"26","author":"Li","year":"2016","journal-title":"Adv. Funct. Mater."},{"key":"ref_132","doi-asserted-by":"crossref","first-page":"111939","DOI":"10.1016\/j.sna.2020.111939","article-title":"Highly sensitive, piezoresistive, silicone\/carbon fiber-based auxetic sensor for low strain values","volume":"305","author":"Taherkhani","year":"2020","journal-title":"Sens. Actuators A Phys."},{"key":"ref_133","doi-asserted-by":"crossref","first-page":"1556","DOI":"10.1039\/C9TC06036G","article-title":"High-performance, biaxially stretchable conductor based on Ag composites and hierarchical auxetic structure","volume":"8","author":"Han","year":"2020","journal-title":"J. Mater. Chem. C"},{"key":"ref_134","doi-asserted-by":"crossref","unstructured":"Farhangdoust, S., Aghaei, S.M., Amirahmadi, M., Pala, N., and Mehrabi, A. (May, January 27). Auxetic MEMS sensor. Proceedings of the Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems 2020, Orange, CA, USA.","DOI":"10.1117\/12.2559330"},{"key":"ref_135","doi-asserted-by":"crossref","first-page":"45007","DOI":"10.1088\/0964-1726\/23\/4\/045007","article-title":"Shape memory polymer hexachiral auxetic structures with tunable stiffness","volume":"23","author":"Rossiter","year":"2014","journal-title":"Smart Mater. Struct."},{"key":"ref_136","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1016\/j.compstruct.2016.11.056","article-title":"Metamaterials with negative Poisson\u2019s ratio and non-positive thermal expansion","volume":"162","author":"Ai","year":"2017","journal-title":"Compos. Struct."},{"key":"ref_137","doi-asserted-by":"crossref","first-page":"2272","DOI":"10.1109\/LRA.2020.2970943","article-title":"Design of deployable soft robots through plastic deformation of kirigami structures","volume":"5","author":"Sedal","year":"2020","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_138","doi-asserted-by":"crossref","first-page":"743","DOI":"10.1557\/adv.2020.185","article-title":"Surface morphing of geometrically patterned active skins","volume":"1\u20138","author":"Park","year":"2020","journal-title":"MRS Adv."},{"key":"ref_139","unstructured":"Dubbelday, P. (1993). Auxetic Materials: An Annotated Bibliography of Materials with Negative Poisson\u2019s Ratio, PN."},{"key":"ref_140","unstructured":"Sevick, E.M., and Williams, D.R.M. (1995, January 13\u201314). Porous membranes with grafted polymers: Valves and sensors. Proceedings of the Materials Research Society Symposium, Boston, MA, USA."},{"key":"ref_141","doi-asserted-by":"crossref","first-page":"84016","DOI":"10.1088\/0964-1726\/22\/8\/084016","article-title":"Smart metamaterials with tunable auxetic and other properties","volume":"22","author":"Grima","year":"2013","journal-title":"Smart Mater. Struct."},{"key":"ref_142","doi-asserted-by":"crossref","first-page":"632","DOI":"10.1126\/science.aar4586","article-title":"Handedness in shearing auxetics creates rigid and compliant structures","volume":"360","author":"Lipton","year":"2018","journal-title":"Science"},{"key":"ref_143","unstructured":"Lipton, J.I., MacCurdy, R., Chin, L., and Rus, D. (2018). Non-Planar Shearing Auxetic Structures, Devices, and Methods. (20180311833A1), U.S. Patent."},{"key":"ref_144","doi-asserted-by":"crossref","first-page":"815","DOI":"10.1002\/adem.201400433","article-title":"Soft actuation of structured cylinders through auxetic behavior","volume":"17","author":"Lazarus","year":"2015","journal-title":"Adv. Eng. Mater."},{"key":"ref_145","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1089\/soro.2018.0163","article-title":"Poisson induced bending actuator for soft robotic systems","volume":"7","author":"Hasse","year":"2020","journal-title":"Soft Robot."},{"key":"ref_146","doi-asserted-by":"crossref","unstructured":"Pfeil, A., Barb\u00e9, L., Wach, B., Bruyas, A., Geiskopf, F., Nierenberger, M., and Renaud, P. (2018;A, January 26\u201329). A 3D-printed needle driver based on auxetic structure and inchworm kinematics. Proceedings of the ASME Design Engineering Technical Conference, Quebec, QC, Canada.","DOI":"10.1115\/DETC2018-85371"},{"key":"ref_147","doi-asserted-by":"crossref","unstructured":"Bonfanti, S., Guerra, R., Clos, F.F., Rayneau-Kirkhope, D., and Zapperi, S. (2020). Automatic Design of Mechanical Metamaterial Actuators. arXiv.","DOI":"10.1038\/s41467-020-17947-2"},{"key":"ref_148","doi-asserted-by":"crossref","first-page":"1606695","DOI":"10.1002\/adfm.201606695","article-title":"Auxetic foam-based contact-mode triboelectric nanogenerator with highly sensitive self-powered strain sensing capabilities to monitor human body movement","volume":"27","author":"Zhang","year":"2017","journal-title":"Adv. Funct. Mater."},{"key":"ref_149","first-page":"90","article-title":"Auxetic cantilever beam energy harvester","volume":"282","author":"Farhangdoust","year":"2020","journal-title":"Sens. Actuators A: Phys."},{"key":"ref_150","doi-asserted-by":"crossref","first-page":"1179","DOI":"10.1002\/er.5010","article-title":"Enhancement of piezoelectric vibration energy harvesting with auxetic boosters","volume":"44","author":"Eghbali","year":"2020","journal-title":"Int. J. Energy Res."},{"key":"ref_151","unstructured":"Evans, K. (2019, August 17). Expanding Blast-Proof Curtain Will Reduce Impact of Bomb Explosions. Available online: https:\/\/epsrc.ukri.org\/newsevents\/casestudies\/blastproofcurtain\/."},{"key":"ref_152","unstructured":"Nagai, K. (1994). Narrow passage moving body structure. (JP06137799), Japan Patent."},{"key":"ref_153","first-page":"12","article-title":"A growth industry","volume":"8","author":"Stott","year":"2000","journal-title":"Mater. World"},{"key":"ref_154","unstructured":"Ma, Z., Arbor, A., and Hulbert, G.M. (2010). Functionally-graded Npr (Negative Poisson\u2019s Ratio) material for a blast-protective deflector. Eng. Technol."},{"key":"ref_155","doi-asserted-by":"crossref","first-page":"589216","DOI":"10.1155\/2013\/589216","article-title":"A comparative study of ballistic resistance of sandwich panels with aluminum foam and auxetic honeycomb cores","volume":"2013","author":"Yang","year":"2013","journal-title":"Adv. Mech. Eng."},{"key":"ref_156","doi-asserted-by":"crossref","first-page":"589216","DOI":"10.1155\/2013\/892781","article-title":"Ballistic resistance of honeycomb sandwich panels under in-plane high-velocity impact","volume":"2013","author":"Qi","year":"2013","journal-title":"Sci. World J."},{"key":"ref_157","doi-asserted-by":"crossref","first-page":"111838","DOI":"10.1016\/j.compstruct.2019.111838","article-title":"Anti-impact behavior of auxetic sandwich structure with braided face sheets and 3D re-entrant cores","volume":"236","author":"Madke","year":"2020","journal-title":"Compos. Struct."},{"key":"ref_158","doi-asserted-by":"crossref","unstructured":"Luo, F., Zhang, S., and Yang, D. (2020). Anti-explosion performance of composite blastwall with an auxetic re-entrant honeycomb core for offshore platforms. J. Mar. Sci. Eng., 8.","DOI":"10.3390\/jmse8030182"},{"key":"ref_159","doi-asserted-by":"crossref","unstructured":"Lan, X.K., Huang, Q., Zhou, T., and Feng, S. (2020). Optimal design of a novel cylindrical sandwich panel with double arrow auxetic core under air blast loading. Def. Technol.","DOI":"10.1016\/j.dt.2019.09.010"},{"key":"ref_160","unstructured":"(2020, May 13). Auxetix. Available online: https:\/\/www.auxetix.com\/."},{"key":"ref_161","doi-asserted-by":"crossref","unstructured":"Chen, Z., Wu, X., Wang, Z., and Shao, J. (2020). Concepts for morphing airfoil using novel auxetic lattices. Lecture Notes in Electrical Engineering, Springer.","DOI":"10.1007\/978-981-15-1773-0_20"},{"key":"ref_162","doi-asserted-by":"crossref","first-page":"107017","DOI":"10.1016\/j.engfracmech.2020.107017","article-title":"Auxetic behavior of Beishan granite after thermal treatment: A microcracking perspective","volume":"231","author":"Zhao","year":"2020","journal-title":"Eng. Fract. Mech."},{"key":"ref_163","doi-asserted-by":"crossref","first-page":"11002","DOI":"10.1063\/1.4812323","article-title":"Commentary: The materials project: A materials genome approach to accelerating materials innovation","volume":"1","author":"Jain","year":"2013","journal-title":"APL Mater."},{"key":"ref_164","doi-asserted-by":"crossref","first-page":"314","DOI":"10.1016\/j.commatsci.2012.10.028","article-title":"Python materials genomics (pymatgen): A robust, open-source python library for materials analysis","volume":"68","author":"Ong","year":"2013","journal-title":"Comput. Mater. Sci."},{"key":"ref_165","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1007\/s40192-017-0089-0","article-title":"Materials knowledge systems in python\u2014A data science framework for accelerated development of hierarchical materials","volume":"6","author":"Brough","year":"2017","journal-title":"Integr. Mater. Manuf. Innov."},{"key":"ref_166","doi-asserted-by":"crossref","first-page":"1465","DOI":"10.1002\/pssb.201451732","article-title":"Models for the prediction of Poisson\u2019s ratio in the \u201c\u03b1-cristobalite\u201d tetrahedral framework","volume":"252","author":"Alderson","year":"2015","journal-title":"Phys. Status Solidi Basic Res."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/11\/3132\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:34:44Z","timestamp":1760175284000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/11\/3132"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,6,1]]},"references-count":166,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2020,6]]}},"alternative-id":["s20113132"],"URL":"https:\/\/doi.org\/10.3390\/s20113132","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,6,1]]}}}